11:00 AM - 11:15 AM
[STT44-02] Improving the performance of maximum amplitude forecast immediately after the mainshock by introducing a prior distribution
Keywords:Extreme value statistics, Interval maximum amplitude, Prior distribution, Forecast of maximum amplitude, Aftershocks
As significant number of aftershocks occur after a large earthquake, their seismic waves overlap in seismograms and phase picking becomes difficult. Consequently, earthquake catalog tends to deteriorate after a large earthquake. On the other hand, interval maximum amplitudes (IMA) of a seismogram are rarely disturbed by the overlap effect. Considering that IMAs follow the non-stationary Frechet distribution (NFD), Sawazaki (2021) proposed to apply the extreme value analysis to the IMAs to forecast maximum amplitude at each seismic station in the early stage after a mainshock. However, available number of IMAs is usually not sufficient to stabilize the forecast performance immediately after a mainshock. To overcome this issue, in this study, we introduced a prior distribution for estimation of the NFD parameters considering previous aftershock sequences. More precisely, the prior distribution was introduced for p- and c-values of the Omori-Utsu law and m-value of the Ishimoto-Iida law. Moreover, by using the Markov-Chain-Monte-Carlo (MCMC) method, we computed the number of occurrence and probability that IMA exceeds a threshold value, and evaluate the forecast performance through comparison with the observed values.
We used in total 12 IMA traces from Hi-net seismograms for aftershock sequences of the 2008 Iwate-Miyagi earthquake (MJ7.2), the largest foreshock (MJ6.5) and the mainshock (MJ7.3) of the 2016 Kumamoto earthquake, and the 2018 N. Osaka prefecture earthquake (MJ6.1). We computed three-components vector sum of the seismogram and computed the maximum amplitude every 1 minute. The data with saturated amplitude were replaced with the KiK-net borehole seismogram as much as possible. Applying the extreme value analysis to the IMAs every one hour, we estimated parameters of NFD and computed number and probability of future maximum amplitudes. The prior distribution was set according to Omi et al. (2015).
Thanks to the introduced prior distribution, we confirmed that the parameter estimation and the forecast result were stabilized within one hour of the mainshock. Using IMAs obtained within one hour of the mainshock, we calculated number of amplitudes with 0.1 cm/s or more by one day of the mainshock. The score showed that observed number fells within the range of twice and half of the median value of the forecast number for 10 out of 12 IMA traces. Also, 11 out of 12 IMA traces showed that observed number fell within 5% and 95% percentiles of the forecast number.
We also computed the probability that at least one IMA exceeds the mainshock amplitude by 1 day of the mainshock. From IMAs obtained within one hour, the computed probabilities were less than 33% for all the traces except for the two stations for the largest Kumamoto foreshock, which were 67% and 83%. From the IMAs obtained within 6 hours, the probabilities were less than 13 % except for 68% and 86% for the largest Kumamoto foreshock. Actually, among the examined four mainshocks, only the largest Kumamoto foreshock was followed by the larger earthquake (28 hours later). Such specificity in the largest Kumamoto foreshock was also pointed out from the catalog analysis by Omi et al. (2019). We also found that m-value was significantly lower for aftershocks of the largest Kumamoto foreshock. As m-value is proportional to b-value of the Gutenberg-Richter law, this result indicates significantly low b-value for this aftershock sequence.
Acknowledgements: This study is funded by the Japan Society for Promotion of Science (Grant-No. 21K03686).
We used in total 12 IMA traces from Hi-net seismograms for aftershock sequences of the 2008 Iwate-Miyagi earthquake (MJ7.2), the largest foreshock (MJ6.5) and the mainshock (MJ7.3) of the 2016 Kumamoto earthquake, and the 2018 N. Osaka prefecture earthquake (MJ6.1). We computed three-components vector sum of the seismogram and computed the maximum amplitude every 1 minute. The data with saturated amplitude were replaced with the KiK-net borehole seismogram as much as possible. Applying the extreme value analysis to the IMAs every one hour, we estimated parameters of NFD and computed number and probability of future maximum amplitudes. The prior distribution was set according to Omi et al. (2015).
Thanks to the introduced prior distribution, we confirmed that the parameter estimation and the forecast result were stabilized within one hour of the mainshock. Using IMAs obtained within one hour of the mainshock, we calculated number of amplitudes with 0.1 cm/s or more by one day of the mainshock. The score showed that observed number fells within the range of twice and half of the median value of the forecast number for 10 out of 12 IMA traces. Also, 11 out of 12 IMA traces showed that observed number fell within 5% and 95% percentiles of the forecast number.
We also computed the probability that at least one IMA exceeds the mainshock amplitude by 1 day of the mainshock. From IMAs obtained within one hour, the computed probabilities were less than 33% for all the traces except for the two stations for the largest Kumamoto foreshock, which were 67% and 83%. From the IMAs obtained within 6 hours, the probabilities were less than 13 % except for 68% and 86% for the largest Kumamoto foreshock. Actually, among the examined four mainshocks, only the largest Kumamoto foreshock was followed by the larger earthquake (28 hours later). Such specificity in the largest Kumamoto foreshock was also pointed out from the catalog analysis by Omi et al. (2019). We also found that m-value was significantly lower for aftershocks of the largest Kumamoto foreshock. As m-value is proportional to b-value of the Gutenberg-Richter law, this result indicates significantly low b-value for this aftershock sequence.
Acknowledgements: This study is funded by the Japan Society for Promotion of Science (Grant-No. 21K03686).